Definitions and Fixedness
Sometimes we have a fear of fixing the meaning of an idea. We think that while our idea remains unfixed, it has maximum potential and scope.
Everyone else is left with the problem of interpreting our idea. When trying to build things together, this ambiguity can be a significant impediment to progress.
This problem often manifests as a discomfort with definitions. The worry is that a definition can fix an idea in the wrong state, or deprive us of access to many (implicit) definitions at once.
It’s generally better to know what we’re communicating about. There are many kinds of definition that can help us achieve this, and any particular definition does not have to remain fixed.
Pointing
When I worked on construction sites with my brother – a painter – he would say things like:
“Sand the architrave1.”
“Paint the plinth2.”
At first, I didn’t know what he was talking about.
He would then just point at the thing and say: “That.”
In this way, he connected the term and the concept. This was sufficient for me to get the work done.
My brother had given an ostensive definition.
Not every thing is as easy to point at, like invisible atoms, abstract concepts and future solutions.
Even if we can point at something, we may not have sufficient understanding to solve certain problems relating to that thing.
If I can sand an architrave it does not mean I can design an algorithm for creating varied architrave designs. For that, I would need a more precise formulation of the idea.
An ostensive definition can sometimes take the form of exemplars:
My definition of “robust” is that codebase
An exemplar of a concept (good writing) is not the same as a concrete instantiation (sanded architrave). It exemplifies by adhering to some profile of attributes, which may go unstated:
…it has stood the test of time… it is used in production… it hasn’t had a serious bug in years… it is all the foregoing…
We might find it easier to point to good writing if we have have need explicit with each other about our notion of “goodness”.
Dictioneering
The concept of a definition is often associated with the lexical definition. This is the kind of definition that we find in a dictionary.
When I taught science at university, I would sometimes ask students to define a technical concept like “micelle”.
This would prompt a non-trivial number of students to report back a dictionary definition, like this one from Merriam-Webster:
Unit of structure built up from polymeric molecules or ions, such as:
- an ordered region in a fiber (as of cellulose or rayon)
- a molecular aggregate that constitutes a colloidal particle
Of course, I was asking for something more than a dictionary definition.
Armed with a dictionary definition, someone has a basic idea of what is being referred to when a term is used in a conventional way.
A university graduate or skilled professional usually has knowledge of a particular subject far beyond the conventional meaning. The usage of an expert or craftsperson may even deviate substantially from the everyday sense of a term3.
The best students defined the concept of a micelle in relation to the coursework that was being examined. They needed to develop a definition that was more precise to our shared context.
Precising
When building something – like a new technology – we might ask for it to be made more “simple”.
What does “simple” mean here? We could refer to the entries in Merriam-Webster and they wouldn’t help us very much.
We need a precising definition. This makes some general definition more precise to our specific context. We might want a simple technology to conform to some of the following precising definitions:
- A simple technology has the minimum necessary components, to improve our capacity to maintain it
- A simple technology hides the internal complexity of the system, to provide an accessible user interface
- (1) and (2): A simple technology has the minimum necessary components, to improve our capacity to maintain it and so it is accessible to the user
Many other definitions could be imagined and combined.
Precising definitions – and others: like stipulations – are often ameliorative. They make an idea more suited to our purpose or more useful to achieve some goal.
Forming a definition may therefore be a normative act, not merely a descriptive one.
Fact
An act is normative when it relates to values. For example, we might opt for something more beautiful, moral or useful.
Milk can be defined conventionally as a nutritious white liquid or in the language of colloid science an oil-in-water emulsion. When a food scientist knows that milk can be precisely define as an emulsion, they can apply general principles from colloid science to understand that system – this is valuable because the scientist value specific goals, like measurement, prediction and understanding.
Stipulating
To overcome obstacles we sometimes need a stipulative definition.
Conceptual obstacles can include:
- Not knowing how or why to begin a project
- Lacking a shared understanding of a system
- A philosophical impasse about our goals
A stipulation can be provisional and even false but still valuable. The value of the stipulation is as much about the process that it initiates and its foundational role in the building of a cohesive structure or paradigm.
If someone confuses your stipulation for an absolute definition then the exchange of ideas may prematurely collapse, so you need to communicate your intention.
Stipulating a flat world could be an interesting design prompt. It should be minimally controversial as long as people know that you are talking about game development and not geophysics.
world_is_flat = false // it's OK to change your mind
A stipulation can be thought of as a What if? question:
What if x? What follows when x? What can we build, given x?
Operationalising
When I worked in food science laboratories, I said things like:
For the sample vegan cheese replacers, “melted” was defined as the state when the G“ value is observed to exceed the G’ value during oscillatory shear
This is an operational definition, which makes a concept easier to measure and/or quantify. In this case, it makes it easy for those versed in rheology4, who know that G“ and G’ represent liquid-like and solid-like behaviour, to quantify melting.
One of the most famous operational definitions is associated with Alan Turing, and can be stated as:
A machine is intelligent if and only if a human evaluator cannot distinguish between the machine and its human interlocutor when reviewing a text transcript of their conversation
Turing devised his theoretical test of machine intelligence because he considered the contemporary philosophical debates on the matter to be unproductive.
The Turing test has now been passed many times. This doesn’t mean that machines have become intelligent, only that some meet Turing’s operational definition of machine intelligence.
As we encounter such machine “intelligence”, and become aware of its limitations, we should seek better operational definitions.
If the reasoning behind an operational definition is hidden, it can be truly mysterious:
Each employee is assigned a Performance Index according to a variety of metrics. Individual metrics are suitably weighted based on key stakeholder criteria. The weighted metrics are fed into a sophisticated model validated against our quality indicators.
Such numbers have the appearance of being scientific but – in their remarkable opacity – are entirely impossible to inspect, validate or reproduce, and are therefore quite unscientific.
The value in any operational definition is that it helps us grasp clearly that an idea can be tested, and that the justification for that test is sensible.
We should never mistake an operational definition for the thing itself. This is an error characteristic of scientism, in which the richness of the world is displaced with the contingencies and constraints of the model, laboratory or algorithm.
Acknowledging that definitions are subject to revision or correction can replace one fear in us with another. Instead of an anxiety of fixedness, there is a nihilism of definition, in which we reject the possibility that anything can ever truly be defined.
In either case, this will make us difficult collaborators, and we should become more comforable with the range and limits of definitions.